论文标题
poisson-poincaré减少现场理论
Poisson-Poincaré reduction for Field Theories
论文作者
论文摘要
鉴于在纤维束上的哈密顿系统，汉密尔顿方程有一个泊松协变。当谎言组的lie群自由，正确地保持束纤维和汉密尔顿密度的纤维是g不变的时，我们研究了这种表述的减少，以获得对田间理论的泊松葡萄干的类似物。此过程与通过Legendre转换的Lagrange-Poincaré减少了现场理论。最后，给出了在电场中演变的带电链模型的应用。
Given a Hamiltonian system on a fiber bundle, there is a Poisson covariant formulation of the Hamilton equations. When a Lie group G acts freely, properly, preserving the fibers of the bundle and the Hamiltonian density is G-invariant, we study the reduction of this formulation to obtain an analogue of Poisson-Poincaré reduction for field theories. This procedure is related to the Lagrange-Poincaré reduction for field theories via a Legendre transformation. Finally, an application to a model of a charged strand evolving in an electric field is given.
